A most striking feature of high-Tc cuprate superconductors is the persistence of a gap above the superconducting transition temperature Tc, where an unconventional metallic phase, known as the pseudogap, sets in. The pseudogap is not well understood yet and it is generally believed to be at the roots of the high Tc superconducting mechanism. By exploiting cluster dynamical mean field theory results on the two dimensional Hubbard Model, we show that the pseudogap and the superconducting gap compete for the same electrons, producing an unconventional form of the superconducting pairing that involves electrons in high energy states. We show that these findings leave visible fingerprints in the Raman response, which displays a characteristic peak-dip feature. The good agreement between theoretical and experimental results reveal an unprecedented relationship between the pseudogap and superconducting gap, which eventually boosts up the Tc.